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Computer Graphics Group Department of Computer Science and Engineering http://www.cgg.cvut.cz LCTS: Ray Shooting using Longest Common Traversal Sequences Vlastimil Havran , Jiří Bittner havran @fel.cvut.cz Dept. of Computer Science Czech Technical University in Prague Outline

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Computer Graphics Group

Department of Computer Science and Engineering

http://www.cgg.cvut.cz

LCTS: Ray Shooting using Longest Common Traversal Sequences

Vlastimil Havran, Jiří Bittner

havran@fel.cvut.cz

Dept. of Computer ScienceCzech Technical Universityin Prague

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences


Slide2 l.jpg

Outline

1) Introduction (ray shooting, BSP tree)

2) Key Idea of LCTS

3) Simple LCTS

4) Hierarchical LCTS

5) Improvements for LCTS

6) Application and Results

7) Conclusions and Future Work

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences


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B

A

C

ray

D

1) Introduction - ray shooting

Given a ray, find out the first object intersected.

Input: a scene and a ray

Output: the object C

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences


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4

1

C

2

3

1

D

A

2

A

B

3

4

B

C

C

D

1) Introduction to BSP trees -

construction

y

x

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences


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L

R

L

R

Left only

Left, then right

L

R

L

R

Right only

Right, then left

1) Introduction to BSP trees -

recursive ray traversal algorithm

Interior node of

BSP tree

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences


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4

1

2

3

1

R

L

2

R

L

3

4

B

D

ray

Intersection

found

1) Introduction to BSP trees -

recursive ray traversal algorithm

BSP tree:

A

B

A

y

C

R

R

C2

C1

Left | Right

D

Stack:

x

Left | Right

2

4

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences


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1) Introduction to BSP trees -

Efficiency of ray shooting

Total ray shooting time =

time for ray-object intersection tests +

time for ray traversal of BSP tree

1) Decreasing number of ray-object intersection tests

2) Faster ray-object intersection tests

3) Decreasing number of traversal steps

4) Faster traversal step

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences


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C

R2

R2:

R1:

2

1

1

1

D

R1

A

B

B

B

2

2

2

A

B

y

3

3

3

1

3

A

A

C

D

x

Ray origin

2) LCTS - MAIN IDEA

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences


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C

R2

Traversal History for R2:

Traversal History for R1:

R1, R2:

2

head

head

tail

1

D

R1

B

A

B

A

B

B

A

A

2

A

B

y

tail

3

3

1

SLCTS(R1, R2):

x

head

tail

Ray origin

3) Simple LCTS = sequence of leaves

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences


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1

1

4

4

3

3

B

A

y

R1

2

C

B

A

y

D

2

C

R1

R2

x

R2

D

x

3) Simple LCTS - Problems

1) No common sequence of leaves exists.

2) When accessing SLCTS, object was not found, and traversal has to continue further.

;

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences


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C

Traversal History for R1:

Traversal History for R2:

2

1(R,L)

1(R,L)

1

R2

2(L)

3(R,L)

D

D

D

B

B

B

2

A

B

y

3

R1

3

1

A

C

A

C

D

x

2(R)

3(R,L)

4) Hierarchial LCTS

Ray origin

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences


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1(R,L)

1(R,L)

1

2(L)

3(R,L)

D

B

B

2

3

tail

A

A

C

D

C

2(?)

2(R)

3(R,L)

4) Hierarchial LCTS - contd.

Matching two traversal histories into common one:

Traversal History for R1:

B

D

Common Traversal History

for all rays between R1 and R2:

= HLCTS(R1, R2):

Traversal History for R2:

head

B

D

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences


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HLCTS2

R1

R3

R2

HLCTS1

4) Hierarchical LCTS - contd.

1) Matching traversal histories for two or more rays.

2) Matching traversal histories for rays with the previously constructed common traversal history.

HLCTS1 - constructed from

traversal history of R1 and R2

Ray R3 - traversal uses HLCTS1

HLCTS2 - constructed from

HLCTS1 and

traversal history of R3

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences


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5) Further Improvements of LCTS concept

1) Unification of empty leaves.

2) Common termination object.

3) Initial leaf sequence.

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences


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D

5

B

4

R2

2

tail

Simplified LCTS(R1,R2):

R1

3

2(?)

1

head

tail

2(?)

2(?)

5) Unification of empty leaves

LCTS(R1,R2):

head

A

y

Ray origin

=

C

x

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences


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Simplified LCTS(R1,R2):

head

tail

C

R2

R1

More simplified

LCTS(R1,R2):

= tail

head

C

5) Termination object

D

5

B

A

4

Ray origin

y

2

C

3

1

x

Termination object must be convex !

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences


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HLCTS2

R1

R3

R2

HLCTS1

5) Initial Leaf Sequence -

only for HLCTS

Use: For matching common traversal sequence with

new traversal history of ray.

How: Initial leaf nodes of HLCTS need not be matched,

but they are copied only.

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences


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A

D

5

B

B

4

A

2

y

C

3

1

x

6) LCTS Application and Results

Application - where rays exhibit similarities.

1) Hidden Surface Removal

2) Shooting between

two patches.

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences


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ad 6) Application and Results - contd.

Hidden Surface Removal

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences


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SLCTS + scanline:

SLCTS + two dimensions:

ad 6) Application and Results - contd.

Hidden Surface Removal: four methods

- use of SLCTS and HLCTS

- using LCTS concept in one or two dimensions

SLCTS

SLCTS

5

7

6

SLCTS

1

SLCTS

2

1

2

5

6

15

16

13

3

4

8

9

17

7

18

19

20

10

11

12

21

22

14

3

4

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences


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ad 6) Application and Results - contd.

- Number of traversal steps decreases

typically by more than 60 %.

- Time devoted to ray shooting decreases

typically by 20 %.

- Speedup achieved is scene and resolution

dependent.

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences


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7) Conclusions and Further Work

- New concept of traversal coherence introduced.

(not restricted to BSP tree only.)

- SLCTS and HLCTS.

- Hidden Surface Removal tested.

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences


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7) Further Work

- automatic setting of image resolution for SLCTS.

- application for higher order rays in global

illumination algorithms.

- other image sampling patterns for HLCTS in

hidden surface removal.

- use of LCTS in rendering animation sequences.

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences


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Acknowledgements:

- Eduard Groeller and Jan Prikryl from

Vienna University of Technology.

- Czech-Austrian scientific cooperation grant

Aktion number 1999/17.

- IGP company for partially

sponsoring my visit here.

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences